The 30-year-old will return to his homeland on a permanent basis, after agreeing terms with the reigning Argentinian champions.
Rojo had spent the second half of last season on loan with his first club, Estudiantes, before returning to United, although he played his final game for the Reds in November 2019.
Marcos arrived at Old Trafford from Sporting Lisbon in August 2014, making his debut for the club the following month in a 4-0 Premier League victory over Queens Park Rangers.
He started at left-back in our FA Cup and EFL Cup triumphs at Wembley in 2016 and 2017 respectively, and also won the Community Shield and Europa League during his time with the club, missing the latter final against Ajax due to injury but playing a major part in our route to the Stockholm showpiece event.